Alpha

Alpha#

class brainpy.state.Alpha(in_size, name=None, tau=Quantity(8., "ms"), g_initializer=Constant(value=0. mS))#

Alpha synapse model.

This class implements the alpha function synapse model, which produces a smooth, biologically realistic synaptic conductance waveform. The model is characterized by the differential equation system:

dh/dt = -h/tau dg/dt = -g/tau + h/tau

This produces a response that rises and then falls with a characteristic time constant \(\tau\), with peak amplitude occurring at time \(t = \tau\).

Parameters:

in_size (Union[int, Sequence[int], integer, Sequence[integer]]) – Size of the input.
name (Optional[str]) – Name of the synapse instance.
tau (Union[Array, ndarray, bool, number, bool, int, float, complex, Quantity]) – Time constant of the alpha function in milliseconds.
g_initializer (Union[Array, ndarray, bool, number, bool, int, float, complex, Quantity, Callable]) – Initial value or initializer for synaptic conductance.

g#

Synaptic conductance state variable.

Type:: HiddenState

h#

Auxiliary state variable for implementing the alpha function.

Type:: HiddenState

tau#

Time constant of the alpha function.

Type:: Parameter

See also

Expon: Single-exponential decay synapse.
DualExpon: Dual-exponential synapse with separate rise and decay.
AMPA: AMPA receptor kinetic synapse model.

Notes

The alpha function is defined as g(t) = (t/tau) * exp(1-t/tau) for t ≥ 0. This implementation uses an exponential Euler integration method. The output of this synapse is the conductance value.

References

Examples

>>> import brainpy
>>> import brainstate
>>> import saiunit as u
>>> # Create an alpha synapse with 8 ms time constant
>>> syn = brainpy.state.Alpha(100, tau=8.*u.ms)
>>> syn.init_state(batch_size=1)
>>> # Step the synapse
>>> g = syn.update()

init_state(batch_size=None, **kwargs)[source]#: State initialization function.

reset_state(batch_size=None, **kwargs)[source]#: State resetting function.

Alpha

Contents

Alpha#